Trek articles, books, and fandom often give info that the Detapa Council is full of military members anyway, which is why the military controls the government.
I remember reading most references to Cardassia as being a "military dictatorship"..
However, I decided to go back and review some episodes, and found a lot of interesting tidbits;
In "Chain of Command" Picard states that the military 'took over'.
Madred replies, "... we have mandated agricultural programs.That is what
the military has done for Cardassia."
From "Destiny" :
We would, of course, prefer to operate that way as well... however since the Science Ministry falls under the jurisdiction of the military, we have to follow certain rules.
One of them is not to make any project look...
"unnecessarily" dangerous.
After Gilora reveals the other Cardassian is an Obsidian Order agent sent to sabotage the mission, she states;
My superiors in the science ministry will protect me. Frankly, I think Dejar is in a lot more trouble than I am. The Order doesn't reward
failure.
In "The Cardassians" Bashir asks Dukat a question about who ordered him to abandon Cardassian orphans on Bajor...
GUL DUKAT: The civilian leaders. They...
BASHIR

interrupting, prepared) Excuse me. But if I understand the
Cardassian political system, the civilian leaders have no direct
authority over military officers...
Dukat doesn't deny this, and then asks where Bashir got tutoring about Cardassian social politics..
GUL DUKAT:Well, remind my old friend that the withdrawal from Bajor was a decision made by the civilian leaders... one that I clearly opposed...
and, yes, they were the ones who decided to leave the orphans behind. I've regretted that decision ever since. Thank you for your concern, Doctor..........
One of the things I like about going back and taking a look at episodes to spot something, is how fun it can be when you're looking for some information.
I think the older episodes ironically, gives the most interesting information...
So now later in the same episode, we get to this:
GUL DUKAT: Pa'Dar is an eminent member of the civilian assembly. This matter has generated a great deal of interest at the highest levels of our government.
In this case, it is a classic example of power plays, but it also shows something interesting too- The civilian government calling the shots, and Central Command obeying.